Time-variable transit time distributions and transport: Theory and application to storage-dependent transport of chloride in a watershed

Transport processes and pathways through many hydrodynamic systems vary over time, often driven by variations in total water storage. This paper develops a very general approach to modeling unsteady transport through an arbitrary control volume (such as a watershed) that accounts for temporal variability in the underlying transport dynamics. Controls on the selection of discharge from stored water are encapsulated in probability distributions Q(ST,t) of age-ranked storage S-T (the volume of water in storage ranked from youngest to oldest). This framework is applied to a long-term record of rainfall and streamflow chloride in a small, humid watershed at Plynlimon, UK. While a time-invariant gamma distribution for (Q) produced a good fit to data, the fit was significantly improved when the distribution was allowed to vary with catchment storage. However, the variation was inverse to that of a well-mixed system where storage has a pure dilution effect. Discharge at high storage was predicted to contain a larger fraction of recent event water than at low storage. The effective volume of storage involved in transport was 3411 mm at mean catchment wetness, but declined by 71 mm per 1 mm of additional catchment storage, while the fraction of event water in discharge increased by 1.4%. This inverse storage effect is sufficient to reproduce the observed long-memory 1/f fractal spectral structure of stream chloride. Metrics quantifying the strength and direction of storage effects are proposed as useful signatures, and point toward a unified framework for observing and modeling coupled watershed flow and transport.